1. **Problem statement:** Tina drives 150 km from Cork to Kilkenny, leaving at 7:45 a.m. She stops for 15 minutes to charge her car. The average speed for the whole journey is 60 km/h. 2. **Formula and rules:** Average speed is given by $$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}$$. 3. **Calculate total time:** $$\text{Total time} = \frac{\text{Total distance}}{\text{Average speed}} = \frac{150}{60} = 2.5 \text{ hours}$$ 4. **Convert total time to hours and minutes:** $$2.5 \text{ hours} = 2 \text{ hours } 30 \text{ minutes}$$ 5. **Calculate driving time excluding charging stop:** $$\text{Driving time} = \text{Total time} - \text{Charging time} = 2.5 - \frac{15}{60} = 2.5 - 0.25 = 2.25 \text{ hours}$$ 6. **Calculate arrival time:** Tina leaves at 7:45 a.m. Adding total time 2.5 hours: $$7:45 + 2 \text{ hours } 30 \text{ minutes} = 10:15 \text{ a.m.}$$ --- **Answer to (a):** Tina arrives at Kilkenny at **10:15 a.m.** --- 7. **For part (b)(i):** - Stage A: from 7:45 to 8:45, distance 0 to 100 km (given). - Stage B: from 8:45 to 9:00, stopped, distance constant at 100 km. - Stage C: from 9:00 to arrival at 10:15, distance from 100 km to 150 km. Duration of Stage C: $$10:15 - 9:00 = 1 \text{ hour } 15 \text{ minutes} = 1.25 \text{ hours}$$ Speed during Stage C: $$\frac{150 - 100}{1.25} = \frac{50}{1.25} = 40 \text{ km/h}$$ Draw Stage C as a straight line from (9:00, 100 km) to (10:15, 150 km). --- 8. **For part (b)(ii):** - Stage A speed: $$\frac{100}{1} = 100 \text{ km/h}$$ - Stage B speed: 0 km/h (stopped) - Stage C speed: 40 km/h **Fastest speed is during Stage A.** **Justification:** Stage A has the steepest slope on the distance-time graph, indicating the highest speed of 100 km/h compared to 0 km/h and 40 km/h in other stages.